If $A$ and $B$ are two sets,then $A \cap (A \cup B)'$ is equal to

$H_3BO_3$ is

The product of the distinct $(2n)^{\text{th}}$ roots of $1+i\sqrt{3}$ is equal to:

If $\omega$ is a complex cube root of unity,then $\sin \left\{\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right\}$ is equal to

One turn of insulated wire in the form of a planar square frame with side $l = 0.2\,m$ and resistance $R = 1\,\Omega$ is placed in a uniform magnetic field perpendicular to the plane of the frame. The current passing through the turn when the magnetic field starts to decrease at a constant rate of $0.1\,T/s$ is......$mA$.

The diameter of the objective of a telescope is $1 \ m$. Its resolving limit for light of wavelength $4538 \ \mathring{A}$ will be: